Check that all the fans are running. Check that they all have free airflow.
(I've seen PC's fried that were in dusty/dirty conditions, and the fan air
ports were blocked by dust bunnies.) If all this checks out, check that the
system isn't overclocked, (at least not until you rectify the problem) and
check that there aren't any cooling ducts missing from the original
manufacturing configuration. Brand name systems often use custom ducts to
vent air directly from the CPU - by the time you've gotten this far, you
should have already made sure your CPU fan is working properly. Finally,
find a way to add additional cooling fans to the case. Most aftermarket
cases have room for multiple fans; if not available, there are fans that can
fit into an unused PCI slot.
There are also freezing sprays you can get at electronic shops that you can
spray directly on electronic parts while in use, How they evaporate will
tell you what parts are running hot and help identify a part that is running
hot and failing.